Mean-field theory for the three-dimensional Coulomb glass

We study the low temperature phase of the 3D Coulomb glass within a mean field approach which reduces the full problem to an effective single site model with a non-trivial replica structure. We predict a finite glass transition temperature $T_c$, and a glassy low temperature phase characterized by permanent criticality. The latter is shown to assure the saturation of the Efros-Shklovskii Coulomb gap in the density of states. We find this pseudogap to be universal due to a fixed point in Parisi's flow equations. The latter is given a physical interpretation in terms of a dynamical self-similarity of the system in the long time limit, shedding new light on the concept of effective temperature. From the low temperature solution we infer properties of the hierarchical energy landscape, which we use to make predictions about the master function governing the aging in relaxation experiments.